The home secretary, Theresa May, is struggling to contain the row over border controls after she admitted she had personally authorised their relaxation and evidence emerged suggesting she had given officials the discretion to loosen the rules still further.

May was also forced to admit to the Commons she would never know how many people had been allowed into the UK without proper checks.

The home secretary conceded she had taken the decision in July to sign off a four-month pilot scheme allowing passport checks to be scaled back for European Union passport holders to cope with lengthy airport queues during the peak summer traffic season. She insisted that UK Border Force officials had gone further than she had intended or authorised.

Three senior officials from the border force – including its chief, Brodie Clark – were suspended last week amid claims that May had reacted with "fury" when she discovered the measures had gone beyond those she had authorised. Ministerial sources were quoted then claiming that they were the work of a "rogue civil servant".

But May came under pressure when the shadow home secretary, Yvette Cooper, produced an internal UK Border Agency operational memo in the Commons as evidence that May had "given the green light for weaker controls" despite insisting that senior officials had been acting without ministerial authorisation.

The leaked UKBA interim operational instruction dated 28 July 2011, which is believed have been signed off by Home Office ministers, sets out the agreed measures then clearly states: "If, for whatever reason, it is considered necessary to take further measures, beyond those listed above, local managers must escalate to the Border Force Duty Director to seek authority for their proposed action."

Cooper told May that instruction demonstrated that instead of strengthening Britain's border controls she had decided to water them down as official government policy, even though she had not told parliament.

"She has blamed officials for relaxing the checks further than she intended. But she gave the green light for weaker controls … a green light to experiment with watering down rather than increasing border controls," Cooper said.

Two further leaked emails from July show that immigration officers at Heathrow were ordered to stop routinely asking questions of visa holders – ie non-EU nationals – and evidence that the secretly relaxed vetting regime was linked to staffing shortages.

A Home Office official said the reference to discretion in the leaked operational instruction was "a health and safety measure for when terminals become overcrowded, things like that. That is not part of the pilot. That has been in place since 2007."

The row over the secret relaxation of UK border controls, during a summer when the Conservatives have banged the drum for their "tough" immigration policy, threatens to tarnish May's reputation for competence. This is third time in 18 months she has had to face a Commons row – the first two involved the sex offenders' register and emergency legislation to restore police bail.

Downing Street insisted on Monday that David Cameron had full confidence in May but refused to be drawn on whether he approved of the July decision to relax border checks to cope with lengthening airport security queues.

The home secretary said the pilot project targeted "intelligence-led checks on higher-risk passengers" but officials had gone further and "authorised the wider relaxation of border controls without ministerial sanction".

The extra measures included lifting checks at busy times on biometric passport holders from outside Europe and suspending checks of adults at Calais against the Home Office warnings index or watchlist of potential terrorists and illegal migrants.

The home secretary said as a result of the extra measures "we will never know how many people entered the country who should have been prevented from doing so after being flagged by the warnings index".

She insisted the staff at UKBA had been "let down" by senior officials at the top of their organisation who had put border security at risk and added that those responsible would be punished.

The home secretary claimed her authorisation of relaxed passport regime applied to checks on European children travelling with parents, or other categories who did not pose a credible security risk. Under limited circumstances, officials could also use their discretion on whether to open biometric chips on EU passports to check the second secure photograph.

She insisted that the "authorised regime" came with the backing of the security services.

But the border checks had gone much further and adults had not been checked against the warning index at Calais and fingerprinting of non-European nationals from countries that needed a visa had been "abandoned on a regular basis without ministerial approval".

"I did not give my consent or authorisation for any of these decisions," May told MPs. "Indeed I told officials explicitly that the pilot was to go no further than we had agreed."

The top civil servants' union, the First Division Association, voiced their anger at the suspension of Clark and the two other senior UKBA managers. Clark is one of the Home Office's most experienced civil servants having been in charge of the high security prison estate, the immigration service's detention centres and the operational arm of the UK Border Agency during his Whitehall career that spans at least three decades.

FDA national officer Paul Whiteman said: "It appears that Mr Clark has been found guilty by the home secretary even before he has been asked a single question. FDA members are entitled to expect that they will be allowed the opportunity to respond to any allegations before a secretary of state announces their view as to culpability."

He said Clark was looking forward to co-operating fully with any independent or parliamentary inquiry into these matters, where he would be able to explain the extent of the authority he believed was in place to relax border controls: "That will allow the public and MPs to judge whether events were really as straightforward as described by the home secretary today," said Whiteman.

Three internal Home Office inquiries have been put in train, including a review by the chief inspector of immigration, John Vine, which will look at the role of ministers in the affair. May is due to face further questions before the Commons home affairs committee on the row on Tuesday.